Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 11 x + 43 x^{2} )( 1 - 10 x + 43 x^{2} )$ |
| $1 - 21 x + 196 x^{2} - 903 x^{3} + 1849 x^{4}$ | |
| Frobenius angles: | $\pm0.183291501244$, $\pm0.223975234504$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Cyclic group of points: | yes |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1122$ | $3332340$ | $6351601608$ | $11708643117600$ | $21618240966561822$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $23$ | $1801$ | $79886$ | $3424777$ | $147054413$ | $6321589234$ | $271819047551$ | $11688195573073$ | $502592546846378$ | $21611481844365961$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$| The isogeny class factors as 1.43.al $\times$ 1.43.ak and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 2.43.ab_ay | $2$ | (not in LMFDB) |
| 2.43.b_ay | $2$ | (not in LMFDB) |
| 2.43.v_ho | $2$ | (not in LMFDB) |